Can denticity and hapticity be defined simulaneously for a ligand?

Question

I am freshly studying coordination chemistry.

What I understand from denticity and hapticity is:

Denticity - no. of electron donating sites in a ligand.

Hapticity - no. of electron donating atoms in a pi-bond conjugated ligand.

The use of the terms "sites" in denticity and "atoms" in hapticity makes it possible for a compound to have different denticity and hapticity at the same time. For example: ethylene can should be monodentate and η2. So, my final questions are,

1. Can we define both denticity and hapticity for a pi-bond conjugated ligand?
2. Are they supposed to have the same values?
3. Why was hapticity needed in the first place when one can count the nummber of pi-bonds and define denticity accordingly? Is it because more electrons can be donated by a conjugated system?

Thanks in advance.